Anshuman Baruah

We present a unified topological and geometric analysis of charged Anti-de Sitter (AdS) black holes immersed in a quintessence field, incorporating infrared gravitational corrections arising from the Extended Uncertainty Principle (EUP). The latter modifies the standard Heisenberg uncertainty relation by introducing a minimal momentum/maximal length scale, which effectively captures long-wavelength quantum gravitational effects relevant to black hole thermodynamics in curved spacetimes. We derive analytic expressions for the corrected Hawking temperature, entropy and heat capacity in terms of the EUP deformation parameter. Furthermore, the inclusion of quintessence, characterized by barotropic indices \(ω_q = -\frac{2}{3}\) and \(ω_q = -\frac{1}{3}\), modifies the black hole metric function. By studying the relaxation-time function $τ(r_h)$, we identify a number of inflection points that depends sensitively on the equation of state parameter of quintessence, indicating a nontrivial impact of the latter on the black hole phase structure. Applying Duan's topological current method to the off-shell free energy, we compute integer-valued winding numbers associated with each thermodynamic critical point. A parallel topological analysis of the photon sphere assigns charges \( \pm 1 \) to individual light rings, showing that quintessence effects can trigger the splitting or merging of photon spheres, while preserving the total exterior topological charge of $-1$.

Kalb-Ramond (KR) gravity is an intriguing model incorporating local Lorentz violation, and black hole (BH) solutions are known to exist. In this study, we investigate some crucial aspects of BHs endowed with a global monopole charge in the self-interacting KR field. Specifically, we study the quasinormal modes (QNMs) corresponding to scalar, electromagnetic, and gravitational perturbations; derive rigorous bounds for the greybody factors (GBFs); and examine the sparsity of Hawking radiation. The effects of the model parameters $\ell$ (Lorentz-violating parameter in KR gravity) and $η$ (monopole charge) on these phenomena are elaborated. First, QNMs are evaluated with high precision using the 13\textsuperscript{th}-order Padé-averaged WKB method and cross-examined via time-domain analyses within an acceptable parameter space. The results show that the estimated QNMs are more sensitive to $\ell$; however, both model parameters influence the frequency spectra. The derived bounds on the GBFs aid in further constraining the parameter space. It is shown that $\ell$ and $η$ have a similar effect on the greybody bounds. Furthermore, positive and negative values of $\ell$ have opposing effects in that the bounds are reversed for the two cases. The analyses of the Hawking radiation sparsity highlight the effect of $\ell$, and two scenarios are noted: either the radiation emitted is less sparse than Hawking radiation, or it is more sparse during the evaporation phase. Thus, this work presents a comprehensive account of BHs in KR gravity with a global monopole charge.

Wormhole solutions in General Relativity (GR) require exotic matter sources that violate the null energy condition (NEC), and it is well-known that higher-order modifications of GR and some alternative matter sources can support wormholes. In this study, we explore the possibility of formulating traversable wormholes in f (R) modified gravity, which is perhaps the most widely discussed modification of GR, with two approaches. First, to investigate the effects of geometrical constraints on the global characteristics, we gauge the rr–component of the metric tensor and employ Padè approximation to check whether a well–constrained shape function can be formulated in this manner. We then derive the field equations with a background of string cloud and numerically analyse the energy conditions, stability, and amount of exotic matter in this space-time. Next, as an alternative source in a simple f (R) gravity model, we use the background cloud of strings to estimate the wormhole shape function and analyse the relevant properties of the space-time. These results are then compared with those of wormholes threaded by normal matter in the simple f (R) gravity model considered. The results demonstrate that string cloud is a viable source for wormholes with NEC violations; however, the wormhole space-times in the simple f (R) gravity model considered in this study are unstable. Розв’язання червоточин у загальній теорії відносності (ОТО) потребує \textit{екзотичних} джерел матерії, які порушують умову нульової енергії (NEC), і добре відомо, що модифікації ОТО вищого порядку та деякі альтернативні джерела матерії можуть підтримувати червоточини. У цьому дослідженні ми досліджуємо можливість формулювання прохідних червоточин у $f(R)$ модифікованій гравітації, яка є, мабуть, найбільш обговорюваною модифікацією ОТО, за допомогою двох підходів. По-перше, щоб дослідити вплив геометричних обмежень на глобальні характеристики, ми вимірюємо $rr$--компонент метричного тензора та використовуємо наближення Pad\`{e}, щоб перевірити, чи добре обмежена \textit{функція форми} можна сформулювати таким чином. Потім ми виводимо рівняння поля на тлі струнної хмари та чисельно аналізуємо енергетичні умови, стабільність і кількість екзотичної матерії в цьому просторі-часі. Далі, як альтернативне джерело в простій гравітаційній моделі $f(R)$, ми використовуємо фонову хмару струн для оцінки функції форми червоточини та аналізу відповідних властивостей простору-часу. Потім ці результати порівнюються з даними про червоточини, пронизані нормальною матерією, у простій розглянутій моделі гравітації $f(R)$. Результати демонструють, що струнна хмара є життєздатним джерелом червоточин із порушеннями NEC; однак простір-час червоточини в простій гравітаційній моделі $f(R)$, розглянутій у цьому дослідженні, нестабільний.

Among the several modified/extended gravity paradigms, the concept of antisymmetric connections leading to space-time torsion can be traced back to Cartan. More recently, developments in string theory have suggested the existence of a rank-2 self-interacting tensor field called the Kalb-Ramond field with similar outcomes, the field strength of which can support analytic wormhole-like solutions. However, detailed analyses of the physical properties of interest of such solutions are lacking. In this study, we comprehensively probe the properties of traversable Morris-Thorne like wormhole solutions sourced by the Kalb-Ramond field strength in both General Relativity (GR) and $f(R)$ and $f(R,T)$ modified gravity. We also analyze the coupling of the field strength in GR via a novel non-minimal interaction term in the action. Using suitable parametric constraints in all cases, we evaluate wormhole shape functions, numerically analyze the energy conditions near the throat, check the stability using the generalized Tolman-Oppenheimer-Volkov equation, and demonstrate the possibility of minimum exotic matter by estimating the volume integral quantifier. Our results show the existence of stable wormhole solutions in GR and a simple $f(R,T)$ gravity model, and unstable ones in a power-law type $f(R)$ gravity model.

Traversable wormhole solutions in General Relativity require exotic matter sources that violate the null energy condition (NEC), and such behavior maybe avoided in modified gravity. In this study, we analyze the energy conditions for static, spherically symmetric traversable Morris-Thorne wormholes in a recently proposed viable $f(R)$ gravity model. We numerically analyze solutions considering both constant and variable redshift functions, and present wormhole space-times respecting the NEC, supported by a phantom energy-like equation of state for the source. Moreover, we analyze the stability of the space-times using the generalized Tolman-Oppenheimer-Volkov equation. We demonstrate the effects of certain parameters in the $f(R)$ model in determining energy condition violations, and establish that stable wormholes can be formulated only at the expense of violating the NEC.