Vojtěch Pravda
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Vojtěch Pravda has a total of 36 co-authors. Here are the top co-authors by number of shared publications:
- Alena Pravdová
Institute of Mathematics of the Czech Academy of Sciences
66 shared publications - Marcello Ortaggio
Czech Academy of Sciences
25 shared publications Marcello Ortaggio
Institute of Mathematics Czech Academy of Sciences Žitná 25 115 67 Prague 1 Czech Republic
12 shared publications- Jiri Podolsky
Charles University
10 shared publications - Robert Svarc
Charles University
10 shared publications - Sigbjørn Hervik
Faculty of Science and Technology University of Stavanger N-4036 Stavanger Norway
10 shared publications
Latest Publications
- 14 October 2026
- Published by American Physical Society (APS) in Physical Review D
- Vol. 114 (8) , 084036
Static spherically symmetric Kundt vacuum solutions of higher-derivative gravities
We study static spherically symmetric Kundt solutions to the vacuum field equations of quadratic gravity with a cosmological constant, as well as specific models of six-derivative gravity. In quadratic gravity, we identify all solutions for coupling constants satisfying $\ensuremath{\alpha}\ensuremath{\ne}3\ensuremath{\beta}$, while the case $\ensuremath{\alpha}=3\ensuremath{\beta}$ is studied using the Frobenius method, where we derive the recurrence relations for the power series. In contrast, in six-derivative gravity, we focus on selected models to illustrate the variety of closed-form solutions; we also analyze possible indicial families of Frobenius solutions. For all solutions, we analyze curvature singularities and their accessibility to geodesic observers. We then construct exact gravitational-wave solutions propagating on some of these backgrounds in quadratic and six-derivative gravity. It is known that in Einstein gravity, gravitational waves on the Nariai background unavoidably contain singularities, which are interpreted as physical sources generating these gravitational waves. In contrast, in addition to singular solutions, for appropriate values of the coupling constants, higher-order gravities allow for globally smooth solutions representing gravitational waves.- 14 October 2026
- Published by American Physical Society (APS) in Physical Review D
- Vol. 114 (8) , 084036
Static spherically symmetric Kundt vacuum solutions of higher-derivative gravities
We study static spherically symmetric Kundt solutions to the vacuum field equations of quadratic gravity with a cosmological constant, as well as specific models of six-derivative gravity. In quadratic gravity, we identify all solutions for coupling constants satisfying $\ensuremath{\alpha}\ensuremath{\ne}3\ensuremath{\beta}$, while the case $\ensuremath{\alpha}=3\ensuremath{\beta}$ is studied using the Frobenius method, where we derive the recurrence relations for the power series. In contrast, in six-derivative gravity, we focus on selected models to illustrate the variety of closed-form solutions; we also analyze possible indicial families of Frobenius solutions. For all solutions, we analyze curvature singularities and their accessibility to geodesic observers. We then construct exact gravitational-wave solutions propagating on some of these backgrounds in quadratic and six-derivative gravity. It is known that in Einstein gravity, gravitational waves on the Nariai background unavoidably contain singularities, which are interpreted as physical sources generating these gravitational waves. In contrast, in addition to singular solutions, for appropriate values of the coupling constants, higher-order gravities allow for globally smooth solutions representing gravitational waves.- 20 January 2026
- Published by American Physical Society (APS) in Physical Review D
- Vol. 113 (2)
Vacuum and charged asymptotically (A)dS black holes in quadratic gravity
- 20 January 2026
- Published by American Physical Society (APS) in Physical Review D
- Vol. 113 (2)
Vacuum and charged asymptotically (A)dS black holes in quadratic gravity
- 30 August 2024
- Published by American Physical Society (APS) in Physical Review D
- Vol. 110 (4) , 044069
Charged black holes in quadratic gravity
We study electrically charged, static, spherically symmetric black holes in quadratic gravity using the conformal-to-Kundt technique, which leads to a considerable simplification of the field equations. We study the solutions using a Frobenius-like approach of power-series expansions. The indicial equations restrict the set of possible leading powers to a few cases, describing, e.g., black holes, wormholes, or naked singularities. We focus on the black hole case and derive recurrent formulas for all series coefficients of the infinite power-series expansion around the horizon. The solution is characterized by electric charge , the black-hole radius , and the Bach parameter related to the strength of the Bach tensor at the horizon. However, the Bach parameter has to be fine-tuned to ensure asymptotic flatness. The fine-tuning of for a given and returns up to two values, describing two branches of asymptotically flat, static, spherically symmetric, charged black holes in quadratic gravity. This is in agreement with previous numerical works. We discuss various physical properties of these black holes, such as their asymptotic mass, temperature, photon spheres, and black-hole shadows. A straightforward generalization to dyonic black holes in quadratic gravity is also briefly mentioned.- 30 August 2024
- Published by American Physical Society (APS) in Physical Review D
- Vol. 110 (4) , 044069
Charged black holes in quadratic gravity
We study electrically charged, static, spherically symmetric black holes in quadratic gravity using the conformal-to-Kundt technique, which leads to a considerable simplification of the field equations. We study the solutions using a Frobenius-like approach of power-series expansions. The indicial equations restrict the set of possible leading powers to a few cases, describing, e.g., black holes, wormholes, or naked singularities. We focus on the black hole case and derive recurrent formulas for all series coefficients of the infinite power-series expansion around the horizon. The solution is characterized by electric charge , the black-hole radius , and the Bach parameter related to the strength of the Bach tensor at the horizon. However, the Bach parameter has to be fine-tuned to ensure asymptotic flatness. The fine-tuning of for a given and returns up to two values, describing two branches of asymptotically flat, static, spherically symmetric, charged black holes in quadratic gravity. This is in agreement with previous numerical works. We discuss various physical properties of these black holes, such as their asymptotic mass, temperature, photon spheres, and black-hole shadows. A straightforward generalization to dyonic black holes in quadratic gravity is also briefly mentioned.- Open Access
- 13 February 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (2) , 1-28
Kerr-Schild double copy for Kundt spacetimes of any dimension
We show that vacuum type N Kundt spacetimes in an arbitrary dimension admit a Kerr-Schild (KS) double copy. This is mostly done in a coordinate-independent way using the higher-dimensional Newman-Penrose formalism. We also discuss two kinds of non-uniqueness of an electromagnetic field corresponding to a given KS metric (i.e., its single copy) — these originate, respectively, from the rescaling freedom in the KS vector and from the non-uniqueness of the splitting of the KS metric in the flat part and the KS part. In connection to this, we show that the subset of KS pp-waves admits both null and non-null electromagnetic single copies. Since vacuum type N Kundt spacetimes are universal solutions of virtually any higher-order gravities and null fields in such backgrounds are immune to higher-order electromagnetic corrections, the KS-Kundt double copy demonstrated in the present paper also applies to large classes of modified theories.
- 13 February 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (2) , 1-28
Open AccessKerr-Schild double copy for Kundt spacetimes of any dimension
We show that vacuum type N Kundt spacetimes in an arbitrary dimension admit a Kerr-Schild (KS) double copy. This is mostly done in a coordinate-independent way using the higher-dimensional Newman-Penrose formalism. We also discuss two kinds of non-uniqueness of an electromagnetic field corresponding to a given KS metric (i.e., its single copy) — these originate, respectively, from the rescaling freedom in the KS vector and from the non-uniqueness of the splitting of the KS metric in the flat part and the KS part. In connection to this, we show that the subset of KS pp-waves admits both null and non-null electromagnetic single copies. Since vacuum type N Kundt spacetimes are universal solutions of virtually any higher-order gravities and null fields in such backgrounds are immune to higher-order electromagnetic corrections, the KS-Kundt double copy demonstrated in the present paper also applies to large classes of modified theories.
- Open Access
Kerr-Schild double copy for Kundt spacetimes of any dimension
We show that vacuum type N Kundt spacetimes in an arbitrary dimension admit a Kerr-Schild (KS) double copy. This is mostly done in a coordinate-independent way using the higher-dimensional Newman-Penrose formalism. We also discuss two kinds of non-uniqueness of an electromagnetic field corresponding to a given KS metric (i.e., its single copy) - these originate, respectively, from the rescaling freedom in the KS vector and from the non-uniqueness of the splitting of the KS metric in the flat part and the KS part. In connection to this, we show that the subset of KS pp-waves admits both null and non-null electromagnetic single copies. Since vacuum type N Kundt spacetimes are universal solutions of virtually any higher-order gravities and null fields in such backgrounds are immune to higher-order electromagnetic corrections, the KS-Kundt double copy demonstrated in the present paper also applies to large classes of modified theories.
Open AccessKerr-Schild double copy for Kundt spacetimes of any dimension
We show that vacuum type N Kundt spacetimes in an arbitrary dimension admit a Kerr-Schild (KS) double copy. This is mostly done in a coordinate-independent way using the higher-dimensional Newman-Penrose formalism. We also discuss two kinds of non-uniqueness of an electromagnetic field corresponding to a given KS metric (i.e., its single copy) - these originate, respectively, from the rescaling freedom in the KS vector and from the non-uniqueness of the splitting of the KS metric in the flat part and the KS part. In connection to this, we show that the subset of KS pp-waves admits both null and non-null electromagnetic single copies. Since vacuum type N Kundt spacetimes are universal solutions of virtually any higher-order gravities and null fields in such backgrounds are immune to higher-order electromagnetic corrections, the KS-Kundt double copy demonstrated in the present paper also applies to large classes of modified theories.
- Open Access
- 25 February 2023
- Published by Springer Nature in The European Physical Journal C
- Vol. 83 (2) , 1-12
Topological black holes in higher derivative gravity
We study static black holes in quadratic gravity with planar and hyperbolic symmetry and non-extremal horizons. We obtain a solution in terms of an infinite power-series expansion around the horizon, which is characterized by two independent integration constants – the black hole radius and the strength of the Bach tensor at the horizon. While in Einstein’s gravity, such black holes require a negative cosmological constant $$\Lambda $$ , in quadratic gravity they can exist for any sign of $$\Lambda $$ and also for $$\Lambda =0$$ . Different branches of Schwarzschild–Bach–(A)dS or purely Bachian black holes are identified which admit distinct Einstein limits. Depending on the curvature of the transverse space and the value of $$\Lambda $$ , these Einstein limits result in (A)dS–Schwarzschild spacetimes with a transverse space of arbitrary curvature (such as black holes and naked singularities) or in Kundt metrics of the (anti-)Nariai type (i.e., dS $$_2\times $$ S $$^2$$ , AdS $$_2\times $$ H $$^2$$ , and flat spacetime). In the special case of toroidal black holes with $$\Lambda =0$$ , we also discuss how the Bach parameter needs to be fine-tuned to ensure that the metric does not blow up near infinity and instead matches asymptotically a Ricci-flat solution.- 25 February 2023
- Published by Springer Nature in The European Physical Journal C
- Vol. 83 (2) , 1-12
Open AccessTopological black holes in higher derivative gravity
We study static black holes in quadratic gravity with planar and hyperbolic symmetry and non-extremal horizons. We obtain a solution in terms of an infinite power-series expansion around the horizon, which is characterized by two independent integration constants – the black hole radius and the strength of the Bach tensor at the horizon. While in Einstein’s gravity, such black holes require a negative cosmological constant $$\Lambda $$ , in quadratic gravity they can exist for any sign of $$\Lambda $$ and also for $$\Lambda =0$$ . Different branches of Schwarzschild–Bach–(A)dS or purely Bachian black holes are identified which admit distinct Einstein limits. Depending on the curvature of the transverse space and the value of $$\Lambda $$ , these Einstein limits result in (A)dS–Schwarzschild spacetimes with a transverse space of arbitrary curvature (such as black holes and naked singularities) or in Kundt metrics of the (anti-)Nariai type (i.e., dS $$_2\times $$ S $$^2$$ , AdS $$_2\times $$ H $$^2$$ , and flat spacetime). In the special case of toroidal black holes with $$\Lambda =0$$ , we also discuss how the Bach parameter needs to be fine-tuned to ensure that the metric does not blow up near infinity and instead matches asymptotically a Ricci-flat solution. - Open Access
On well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta
We study various mathematical aspects of the charged rotating black hole with two equal-magnitude angular momenta in five dimensions. We introduce a coordinate system that is regular on the horizon and in which Einstein-Maxwell equations reduce to an autonomous system of ODEs. Employing Bondi and Kruskal-like coordinates, we analyze the geometric regularity of the black hole metric at infinity and the horizon, respectively, and the well-posedness of the corresponding boundary value problem. We also study the algebraic types of the electromagnetic and curvature tensors. While outside the horizon the electromagnetic and Ricci tensors are of type D, the Weyl tensor is algebraically general. The Weyl tensor simplifies to type~II on the horizon and type~D on the bifurcation sphere. These results imply inconsistency of the metric with the Kerr--Schild form with a geodesic Kerr-Schild vector. This feature is shared by the four-dimensional Kerr-Newman metric and the vacuum Myers-Perry or charged Schwarzschild-Tangherlini geometries in arbitrary dimension, but hence not by the black hole we have considered here.
Open AccessOn well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta
We study various mathematical aspects of the charged rotating black hole with two equal-magnitude angular momenta in five dimensions. We introduce a coordinate system that is regular on the horizon and in which Einstein-Maxwell equations reduce to an autonomous system of ODEs. Employing Bondi and Kruskal-like coordinates, we analyze the geometric regularity of the black hole metric at infinity and the horizon, respectively, and the well-posedness of the corresponding boundary value problem. We also study the algebraic types of the electromagnetic and curvature tensors. While outside the horizon the electromagnetic and Ricci tensors are of type D, the Weyl tensor is algebraically general. The Weyl tensor simplifies to type~II on the horizon and type~D on the bifurcation sphere. These results imply inconsistency of the metric with the Kerr--Schild form with a geodesic Kerr-Schild vector. This feature is shared by the four-dimensional Kerr-Newman metric and the vacuum Myers-Perry or charged Schwarzschild-Tangherlini geometries in arbitrary dimension, but hence not by the black hole we have considered here.
- Open Access
- 10 March 2022
- Published by Springer Nature in The European Physical Journal C
- Vol. 82 (3) , 1-20
On well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta
We study various mathematical aspects of the charged rotating black hole with two equal-magnitude angular momenta in five dimensions. We introduce a coordinate system that is regular on the horizon and in which Einstein–Maxwell equations reduce to an autonomous system of ODEs. Employing Bondi and Kruskal-like coordinates, we analyze the geometric regularity of the black hole metric at infinity and the horizon, respectively, and the well-posedness of the corresponding boundary value problem. We also study the algebraic types of the electromagnetic and curvature tensors. While outside the horizon the electromagnetic and Ricci tensors are of type D, the Weyl tensor is algebraically general. The Weyl tensor simplifies to type II on the horizon and type D on the bifurcation sphere. These results imply inconsistency of the metric with the Kerr–Schild form with a geodesic Kerr–Schild vector. This feature is shared by the four-dimensional Kerr–Newman metric and the vacuum Myers–Perry or charged Schwarzschild–Tangherlini geometries in arbitrary dimension, but hence not by the black hole we have considered here.
- 10 March 2022
- Published by Springer Nature in The European Physical Journal C
- Vol. 82 (3) , 1-20
Open AccessOn well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta
We study various mathematical aspects of the charged rotating black hole with two equal-magnitude angular momenta in five dimensions. We introduce a coordinate system that is regular on the horizon and in which Einstein–Maxwell equations reduce to an autonomous system of ODEs. Employing Bondi and Kruskal-like coordinates, we analyze the geometric regularity of the black hole metric at infinity and the horizon, respectively, and the well-posedness of the corresponding boundary value problem. We also study the algebraic types of the electromagnetic and curvature tensors. While outside the horizon the electromagnetic and Ricci tensors are of type D, the Weyl tensor is algebraically general. The Weyl tensor simplifies to type II on the horizon and type D on the bifurcation sphere. These results imply inconsistency of the metric with the Kerr–Schild form with a geodesic Kerr–Schild vector. This feature is shared by the four-dimensional Kerr–Newman metric and the vacuum Myers–Perry or charged Schwarzschild–Tangherlini geometries in arbitrary dimension, but hence not by the black hole we have considered here.
- Open Access
Black holes and other spherical solutions in quadratic gravity with a cosmological constant
We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant $\Lambda$. Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant throughout a spacetime. Furthermore, we employ the conformal-to-Kundt metric ansatz that is valid for all static spherically symmetric spacetimes and leads to a considerable simplification of the field equations. We arrive at a set of two ordinary differential equations and study its solutions using the Frobenius-like approach of (infinite) power series expansions. While the indicial equations considerably restrict the set of possible leading powers, careful analysis of higher-order terms is necessary to establish the existence of the corresponding classes of solutions. We thus obtain various non-Einstein generalizations of the Schwarzschild, (anti-)de Sitter [or (A)dS for short], Nariai, and Pleba\'{n}ski-Hacyan spacetimes. Interestingly, some classes of solutions allow for an arbitrary value of $\Lambda$, while other classes admit only discrete values of $\Lambda$. For most of these classes, we give recurrent formulas for all series coefficients. We determine which classes contain the Schwarzschild-(A)dS black hole as a special case and briefly discuss the physical interpretation of the spacetimes. In the discussion of physical properties, we naturally focus on the generalization of the Schwarzschild-(A)dS black hole, namely the Schwarzschild-Bach-(A)dS black hole, which possesses one additional Bach parameter. We also study its basic thermodynamical properties and observable effects on test particles caused by the presence of the Bach tensor. This work is a considerable extension of our letter [Phys. Rev. Lett., 121, 231104, 2018].Open AccessBlack holes and other spherical solutions in quadratic gravity with a cosmological constant
We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant $\Lambda$. Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant throughout a spacetime. Furthermore, we employ the conformal-to-Kundt metric ansatz that is valid for all static spherically symmetric spacetimes and leads to a considerable simplification of the field equations. We arrive at a set of two ordinary differential equations and study its solutions using the Frobenius-like approach of (infinite) power series expansions. While the indicial equations considerably restrict the set of possible leading powers, careful analysis of higher-order terms is necessary to establish the existence of the corresponding classes of solutions. We thus obtain various non-Einstein generalizations of the Schwarzschild, (anti-)de Sitter [or (A)dS for short], Nariai, and Pleba\'{n}ski-Hacyan spacetimes. Interestingly, some classes of solutions allow for an arbitrary value of $\Lambda$, while other classes admit only discrete values of $\Lambda$. For most of these classes, we give recurrent formulas for all series coefficients. We determine which classes contain the Schwarzschild-(A)dS black hole as a special case and briefly discuss the physical interpretation of the spacetimes. In the discussion of physical properties, we naturally focus on the generalization of the Schwarzschild-(A)dS black hole, namely the Schwarzschild-Bach-(A)dS black hole, which possesses one additional Bach parameter. We also study its basic thermodynamical properties and observable effects on test particles caused by the presence of the Bach tensor. This work is a considerable extension of our letter [Phys. Rev. Lett., 121, 231104, 2018]. - 23 March 2021
- Published by American Physical Society (APS) in Physical Review D
- Vol. 103 (6) , 064049
Black holes and other spherical solutions in quadratic gravity with a cosmological constant
We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant . Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant throughout a spacetime. Furthermore, we employ the conformal-to-Kundt metric ansatz that is valid for all static spherically symmetric spacetimes and leads to a considerable simplification of the field equations. We arrive at a set of two ordinary differential equations and study its solutions using the Frobenius-like approach of (infinite) power series expansions. While the indicial equations considerably restrict the set of possible leading powers, careful analysis of higher-order terms is necessary to establish the existence of the corresponding classes of solutions. We thus obtain various non-Einstein generalizations of the Schwarzschild, (anti-)de Sitter [or (A)dS for short], Nariai, and Plebański-Hacyan spacetimes. Interestingly, some classes of solutions allow for an arbitrary value of , while other classes admit only discrete values of . For most of these classes, we give recurrent formulas for all series coefficients. We determine which classes contain the Schwarzschild-(A)dS black hole as a special case and briefly discuss the physical interpretation of the spacetimes. In the discussion of physical properties, we naturally focus on the generalization of the Schwarzschild-(A)dS black hole, namely the Schwarzschild-Bach-(A)dS black hole, which possesses one additional Bach parameter. We also study its basic thermodynamical properties and observable effects on test particles caused by the presence of the Bach tensor. This work is a considerable extension of our Letter [ Phys. Rev. Lett. 121, 231104 (2018)].- 23 March 2021
- Published by American Physical Society (APS) in Physical Review D
- Vol. 103 (6) , 064049
Black holes and other spherical solutions in quadratic gravity with a cosmological constant
We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant . Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant throughout a spacetime. Furthermore, we employ the conformal-to-Kundt metric ansatz that is valid for all static spherically symmetric spacetimes and leads to a considerable simplification of the field equations. We arrive at a set of two ordinary differential equations and study its solutions using the Frobenius-like approach of (infinite) power series expansions. While the indicial equations considerably restrict the set of possible leading powers, careful analysis of higher-order terms is necessary to establish the existence of the corresponding classes of solutions. We thus obtain various non-Einstein generalizations of the Schwarzschild, (anti-)de Sitter [or (A)dS for short], Nariai, and Plebański-Hacyan spacetimes. Interestingly, some classes of solutions allow for an arbitrary value of , while other classes admit only discrete values of . For most of these classes, we give recurrent formulas for all series coefficients. We determine which classes contain the Schwarzschild-(A)dS black hole as a special case and briefly discuss the physical interpretation of the spacetimes. In the discussion of physical properties, we naturally focus on the generalization of the Schwarzschild-(A)dS black hole, namely the Schwarzschild-Bach-(A)dS black hole, which possesses one additional Bach parameter. We also study its basic thermodynamical properties and observable effects on test particles caused by the presence of the Bach tensor. This work is a considerable extension of our Letter [ Phys. Rev. Lett. 121, 231104 (2018)].