General Relativity and Quantum Cosmology (gr-qc)

Abstract: When a black hole is enclosed in a cavity in asymptotically flat space, an effective volume can be introduced, and an effective pressure can be further defined as its conjugate variable. By this means, an extended phase space is constructed in a cavity, which resembles that in the anti-de Sitter (AdS) space in many aspects. However, there are still some notable dissimilarities simultaneously. In this work, the Joule--Thomson (JT) effect of the black holes, widely discussed in the AdS space as an isenthalpic (constant-mass) process, is shown to only have cooling region in a cavity. On the contrary, in a constant-thermal-energy process (the JT-like effect), there is only heating region in a cavity. Altogether, different from the AdS case, there is no inversion temperature or inversion curve in a cavity. Our work reveals the subtle discrepancy between the two different extended phase spaces that is sensitive to the specific boundary conditions.

Abstract: Colliding or noncolliding plane fronted electromagnetic or gravitational waves are the asymptotic limit of Robinson--Trautman spherical electromagnetic or gravitational waves. Noncolliding plane fronted waves contain no information about their sources whereas colliding waves contain information about possibly the motion of their sources. As a first step to investigate the latter phenomenon we construct an asymptotic limit of Li\'enard--Wiechert electromagnetic fields in the context of Minkowskian space--time. This has the advantage that the source is well known and the calculations can be carried out in full detail. The final result is an algebraically general Maxwell field which consists of colliding plane fronted waves in a subregion of Minkowskian space--time and an interesting byproduct is a novel perspective on a Maxwell field originally discovered by Bateman.

Abstract: In this article, we investigate the bulk-boundary and restricted phase space (RPS) thermodynamics of Rissner-Nordstr\"om (R-N) AdS and 6-dimensional charged Gauss-Bonnet AdS black holes. Also, we examine the topological characteristics of the considered black holes and compare them with the extended thermodynamics results. In fact, we have found that the topological behavior of the bulk-boundary thermodynamics is the same as that of the extended thermodynamics, whereas the RPS thermodynamics exhibits a distinct behavior. We also demonstrate that within the RPS formalism, there is only one critical point with a topological charge of +1 $(Q_t=+1)$. Additionally, for RPS formalism, the inclusion of higher derivative curvature terms in the form of Gauss-Bonnet gravity does not alter the topological classification of critical points in charged AdS black holes.

Abstract: It is well known that, during inflation, the conformal invariance of the electromagnetic action has to be broken in order to produce magnetic fields of observed strengths today. Often, to further enhance the strengths of the magnetic fields, parity is also assumed to be violated when the fields are being generated. In this work, we examine the evolution of the quantum state of the Fourier modes of the non-conformally coupled and parity violating electromagnetic field during inflation. We utilize tools such as the Wigner ellipse, squeezing parameters and quantum discord to understand the evolution of the field. We show that the violation of parity leads to an enhancement of the squeezing amplitude and the quantum discord (or, equivalently, in this context, the entanglement entropy) associated with a pair of opposite wave vectors for one of the two states of polarization (and a suppression for the other state of polarization), when compared to the case wherein parity is conserved. We highlight the similarities between the evolution of the Fourier modes of the electromagnetic field when parity is violated during inflation and the behavior of the modes of a charged, quantum, scalar field in the presence of a constant electric field in a de Sitter universe. We briefly discuss the implications of the results we obtain.

Abstract: Constructing the Hamiltonian in the $\eta$-representation, we explore the geometric phase in the Taub-NUT spacetime, which is spherically symmetric and stationary. The geometric phase around a non-rotating Taub-NUT spacetime reveals both the gravitational analog of Aharonov-Bohm effect and Pancharatnam-Berry phase, similar to the rotating Kerr background. On the other hand, only the latter emerges in the spherically symmetric Schwarzschild geometry as well as in the axisymmetric magnetized Schwarzschild geometry. With this result, we argue that the Aharonov-Bohm effect and Pancharatnam-Berry phase both can emerge in the stationary spacetime, whereas only the latter emerges in the static spacetime. We outline plausible measurements of these effects/phases, mostly for primordial black holes.

Abstract: The low-frequency gravitons correspond to typical wavelengths that left the Hubble radius during the early inflationary stages of expansion and reentered after matter radiation equality. Consequently the temperature and the polarization anisotropies of the cosmic microwave background constrain the tensor-to-scalar-ratio in the aHz region but since the audio band and the MHz domain are sensitive to the post-inflationary expansion rate, the low-frequency determinations of the tensor-to-scalar-ratio can be combined with the high-frequency constraints. In this framework we examine the possibility that the low-frequency gravitons remain invisible in the aHz region but are still potentially detectable at much higher frequencies. Because the number of $e$-folds associated with the exit of the cosmic microwave background wavelengths depends both on the slow-roll parameters and on the total expansion rate after inflation, this approach leads to a set of lower bounds on the tensor-to-scalar-ratio.