Maulik K. Parikh
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Maulik K. Parikh has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Erik Verlinde
Physics Department Princeton University 08544 Princeton NJ
2 shared publications - Ivo Savonije
Spinoza Institute University of Utrecht Utrecht The Netherlands
2 shared publications - Brian R. Greene
Institute for Strings, Cosmology and Astroparticle Physics Department of Physics Columbia University 10027 New York NY USA
1 shared publication - Erik Verlinde
Institute for Theoretical Physics University of Amsterdam Valckenierstraat 65 1018 XE Amsterdam the Netherlands
1 shared publication - Jan Pieter van der Schaar
Institute for Strings, Cosmology and Astroparticle Physics Department of Physics Columbia University 10027 New York NY
1 shared publication
Latest Publications
- Open Access
Universal Correction to the Inflationary Vacuum
The Bunch-Davies state appears precisely thermal to a free-falling observer in de Sitter space. However, precise thermality is unphysical because it violates energy conservation. Instead, the true spectrum must take a certain different form, with the Boltzmann factor $\exp(-\beta \omega_k)$ replaced by $\exp(\Delta S)$, where $S$ is the entropy of the de Sitter horizon. The deviation from precise thermality can be regarded as an explicitly calculable correction to the Bunch-Davies state. This correction is mandatory in that it relies only on energy conservation. The modified Bunch-Davies state leads, in turn, to an ${\cal O} (H/M_p)^2$ modification of the primordial power spectrum of inflationary perturbations, which we determine.Open AccessUniversal Correction to the Inflationary Vacuum
The Bunch-Davies state appears precisely thermal to a free-falling observer in de Sitter space. However, precise thermality is unphysical because it violates energy conservation. Instead, the true spectrum must take a certain different form, with the Boltzmann factor $\exp(-\beta \omega_k)$ replaced by $\exp(\Delta S)$, where $S$ is the entropy of the de Sitter horizon. The deviation from precise thermality can be regarded as an explicitly calculable correction to the Bunch-Davies state. This correction is mandatory in that it relies only on energy conservation. The modified Bunch-Davies state leads, in turn, to an ${\cal O} (H/M_p)^2$ modification of the primordial power spectrum of inflationary perturbations, which we determine. - Open Access
The Volume of Black Holes
We propose a definition of volume for stationary spacetimes. The proposed volume is independent of the choice of stationary time-slicing, and applies even though the Killing vector may not be globally timelike. Moreover, it is constant in time, as well as simple: the volume of a spherical black hole in four dimensions turns out to be just ${4 \over 3} \pi r_+^3$. We then consider whether it is possible to construct spacetimes that have finite horizon area but infinite volume, by sending the radius to infinity while making discrete identifications to preserve the horizon area. We show that, in three or four dimensions, no such solutions exist that are not inconsistent in some way. We discuss the implications for the interpretation of the Bekenstein-Hawking entropy.Open AccessThe Volume of Black Holes
We propose a definition of volume for stationary spacetimes. The proposed volume is independent of the choice of stationary time-slicing, and applies even though the Killing vector may not be globally timelike. Moreover, it is constant in time, as well as simple: the volume of a spherical black hole in four dimensions turns out to be just ${4 \over 3} \pi r_+^3$. We then consider whether it is possible to construct spacetimes that have finite horizon area but infinite volume, by sending the radius to infinity while making discrete identifications to preserve the horizon area. We show that, in three or four dimensions, no such solutions exist that are not inconsistent in some way. We discuss the implications for the interpretation of the Bekenstein-Hawking entropy. - 1 November 2004
- Published by Springer Nature in General Relativity and Gravitation
- Vol. 36 (11) , 2419-2422
A Secret Tunnel Through the Horizon
- 1 November 2004
- Published by Springer Nature in General Relativity and Gravitation
- Vol. 36 (11) , 2419-2422
A Secret Tunnel Through the Horizon
- Open Access
De Sitter Holography with a Finite Number of States
We investigate the possibility that, in a combined theory of quantum mechanics and gravity, de Sitter space is described by finitely many states. The notion of observer complementarity, which states that each observer has complete but complementary information, implies that, for a single observer, the complete Hilbert space describes one side of the horizon. Observer complementarity is implemented by identifying antipodal states with outgoing states. The de Sitter group acts on S-matrix elements. Despite the fact that the de Sitter group has no nontrivial finite-dimensional unitary representations, we show that it is possible to construct an S-matrix that is finite-dimensional, unitary, and de Sitter-invariant. We present a class of examples that realize this idea holographically in terms of spinor fields on the boundary sphere. The finite dimensionality is due to Fermi statistics and an `exclusion principle' that truncates the orthonormal basis in which the spinor fields can be expanded.
Open AccessDe Sitter Holography with a Finite Number of States
We investigate the possibility that, in a combined theory of quantum mechanics and gravity, de Sitter space is described by finitely many states. The notion of observer complementarity, which states that each observer has complete but complementary information, implies that, for a single observer, the complete Hilbert space describes one side of the horizon. Observer complementarity is implemented by identifying antipodal states with outgoing states. The de Sitter group acts on S-matrix elements. Despite the fact that the de Sitter group has no nontrivial finite-dimensional unitary representations, we show that it is possible to construct an S-matrix that is finite-dimensional, unitary, and de Sitter-invariant. We present a class of examples that realize this idea holographically in terms of spinor fields on the boundary sphere. The finite dimensionality is due to Fermi statistics and an `exclusion principle' that truncates the orthonormal basis in which the spinor fields can be expanded.
- Open Access
Energy Conservation and Hawking Radiation
The conservation of energy implies that an isolated radiating black hole cannot have an emission spectrum that is precisely thermal. Moreover, the no-hair theorem is only approximately applicable. We consider the implications for the black hole information puzzle.
Open AccessEnergy Conservation and Hawking Radiation
The conservation of energy implies that an isolated radiating black hole cannot have an emission spectrum that is precisely thermal. Moreover, the no-hair theorem is only approximately applicable. We consider the implications for the black hole information puzzle.
- 20 March 2003
- Published by American Physical Society (APS) in Physical Review D
- Vol. 67 (6) , 064005
Elliptic de Sitter space:We propose that, for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an “elliptic” identification of de Sitter space provides a concrete realization of observer complementarity: every observer has complete information. It is possible to define the analogue of an S matrix for quantum gravity in elliptic de Sitter space that is measurable by all observers. In a holographic description, S-matrix elements may be represented by correlation functions of a dual (conformal field) theory that lives on the single boundary sphere. S-matrix elements are de Sitter invariant, but have different interpretations for different observers. We argue that Hilbert states do not necessarily form representations of the full de Sitter group, but just of the subgroup of rotations. As a result, the Hilbert space can be finite dimensional and still have a positive norm. We also discuss the elliptic interpretation of de Sitter space in the context of type string theory.- 20 March 2003
- Published by American Physical Society (APS) in Physical Review D
- Vol. 67 (6) , 064005
Elliptic de Sitter space:We propose that, for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an “elliptic” identification of de Sitter space provides a concrete realization of observer complementarity: every observer has complete information. It is possible to define the analogue of an S matrix for quantum gravity in elliptic de Sitter space that is measurable by all observers. In a holographic description, S-matrix elements may be represented by correlation functions of a dual (conformal field) theory that lives on the single boundary sphere. S-matrix elements are de Sitter invariant, but have different interpretations for different observers. We argue that Hilbert states do not necessarily form representations of the full de Sitter group, but just of the subgroup of rotations. As a result, the Hilbert space can be finite dimensional and still have a positive norm. We also discuss the elliptic interpretation of de Sitter space in the context of type string theory.- Open Access
Elliptic de Sitter Space: dS/Z_2
We propose that for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an ``elliptic'' $Z_2$-identification of de Sitter space provides a concrete realization of observer complementarity: every observer has complete information. It is possible to define the analog of an S-matrix for quantum gravity in elliptic de Sitter space that is measurable by all observers. In a holographic description, S-matrix elements may be represented by correlation functions of a dual (conformal field) theory that lives on the single boundary sphere. S-matrix elements are de Sitter-invariant, but have different interpretations for different observers. We argue that Hilbert states do not necessarily form representations of the full de Sitter group, but just of the subgroup of rotations. As a result, the Hilbert space can be finite-dimensional and still have positive norm. We also discuss the elliptic interpretation of de Sitter space in the context of type IIB* string theory.
Open AccessElliptic de Sitter Space: dS/Z_2
We propose that for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an ``elliptic'' $Z_2$-identification of de Sitter space provides a concrete realization of observer complementarity: every observer has complete information. It is possible to define the analog of an S-matrix for quantum gravity in elliptic de Sitter space that is measurable by all observers. In a holographic description, S-matrix elements may be represented by correlation functions of a dual (conformal field) theory that lives on the single boundary sphere. S-matrix elements are de Sitter-invariant, but have different interpretations for different observers. We argue that Hilbert states do not necessarily form representations of the full de Sitter group, but just of the subgroup of rotations. As a result, the Hilbert space can be finite-dimensional and still have positive norm. We also discuss the elliptic interpretation of de Sitter space in the context of type IIB* string theory.
- Open Access
New Coordinates for de Sitter Space and de Sitter Radiation
We introduce a simple coordinate system covering half of de Sitter space. The new coordinates have several attractive properties: the time direction is a Killing vector, the metric is smooth at the horizon, and constant-time slices are just flat Euclidean space. We demonstrate the usefulness of the coordinates by calculating the rate at which particles tunnel across the horizon. When self-gravitation is taken into account, the resulting tunneling rate is only approximately thermal. The effective temperature decreases through the emission of radiation.
Open AccessNew Coordinates for de Sitter Space and de Sitter Radiation
We introduce a simple coordinate system covering half of de Sitter space. The new coordinates have several attractive properties: the time direction is a Killing vector, the metric is smooth at the horizon, and constant-time slices are just flat Euclidean space. We demonstrate the usefulness of the coordinates by calculating the rate at which particles tunnel across the horizon. When self-gravitation is taken into account, the resulting tunneling rate is only approximately thermal. The effective temperature decreases through the emission of radiation.