General Relativity and Quantum Cosmology (gr-qc)

Abstract: To comprehend the shadow of a black hole in a general spacetime, we have investigated the concept of the maximal black room (MBR). The boundary of the MBR is a non-spacelike hypersurface that contains at least one null geodesic tangent to its boundary, which we refer to as the rays' surface. Our aim is to explore the geometry of this surface. From our current study, we have observed that the boundary of the MBR is globally unstable. Leveraging this instability, we can determine the boundary based on the physical choice of the initial spacelike hypersurface and the orthogonal condition at that point. Upon examining the existence of the MBR, we can observe that it encompasses any arbitrary black hole. Additionally, we can investigate the possibility of using the MBR to differentiate a black hole from an exotic star with a photon sphere. In spherically symmetric spacetime, subject to energy conditions, the rays' surface encloses a black hole, a naked singularity, or exotic matter that has an inner universe.

Abstract: We show how the Gambier equation arises in connection to Friedmann-Lema$\mbox{\^{i}}$tre-Robertson-Walker (FLRW) cosmology and a Dark Matter equation of state. Moreover, we provide a correspondence between the Friedmann equations and the Gambier equations that possess the Painlev$\acute{\mbox{e}}$ property in $2+1$ dimensions. We also consider special cases of the Gambier G27 equation such as the generalized Pinney equation. For an extended FLRW model with dynamic scalar field as matter model, the Einstein equations correspond to the Milne-Pinney equation which in turn can be mapped to the parametric Gambier equation of second order.

Abstract: We revisit the Kerr black hole as cast in the Boyer-Lindquist, Kerr-Schild and Weyl canonical coordinates, and calculate its total mass/energy and total angular momentum by using linearized gravity along with its background Killing isometries. We argue that the integration of the relevant gravitational flux does not depend on the geometry of the closed and simply connected spatial boundary provided it is also piecewise smooth.

Abstract: The waveform of a binary black hole coalescence appears to be both simple and universal. In this essay we argue that the dynamics should admit a separation into 'fast and slow' degrees of freedom, such that the latter are described by an integrable system of equations, accounting for the simplicity and universality of the waveform. Given that Painlev\'e transcendents are a smoking gun of integrable structures, we propose the Painlev\'e-II transcendent as the key structural element threading a hierarchy of asymptotic models aiming at capturing different (effective) layers in the dynamics. Ward's conjecture relating integrable and (anti)self-dual solutions can provide the avenue to encode background binary black hole data in (non-local) twistor structures.

Abstract: This work is devoted to study the thermodynamic behavior of photon--like particles within the \textit{rainbow} gravity formalism. To to do this, we chose two particular ansatzs to accomplish our calculations. First, we consider a dispersion relation which avoids UV divergences, getting a positive effective cosmological constant. We provide \textit{numerical} analysis for the thermodynamic functions of the system and bounds are estimated. Furthermore, a phase transition is also expected for this model. Second, we consider a dispersion relation employed in the context of \textit{Gamma Ray Bursts}. Remarkably, for this latter case, the thermodynamic properties are calculated in an \textit{analytical} manner and they turn out to depend on the harmonic series $H_{n}$, gamma $\Gamma(z)$, polygamma $\psi_{n}(z)$ and zeta Riemann functions $\zeta(z)$.

Abstract: Physicality has the bad habit of sneaking up on unsuspecting physicists. Unfortunately, it comes in multitudinous incarnations, which will not always make sense in a given situation. Breaching a warp drive metric with physical arguments is all good, but often what counts as physicality here is but a mere mask for something else. In times of analogue space-times and quantum effects, a more open mind is needed. Not only to avoid using a concept of physicality out of its natural habitat, but also to find useful toy models for our enlarged phenomenology of physics with metrics. This journey is bound to be as vexing, confusing, and subtle as it (hopefully) will be illuminating, entertaining, and thought-provoking.

Abstract: We give a simple prescription for relating different solutions to the zero-rest-mass field equations in conformally flat space-time via complex conformal transformations and changes in reality conditions. We give several examples including linearized black holes. In particular, we show that the linearized Plebanski-Demianski and Schwarzschild fields are related by a complex translation and a complex special conformal transformation. Similar results hold for the linearized Kerr and C-metric fields, and for a peculiar toroidal singularity.

Abstract: The main emphasis of this paper is to find the viable solutions of Einstein Maxwell fields equations of compact star in context of modified $f(R)$ theory of gravity. Two different models of modified $f(R)$ gravity are considered. In particular, we choose isotropic matter distribution and Bardeen's model for compact star to find the boundary conditions as an exterior space-time geometry. We use the conformal Killing geometry to compute the metric potentials. We discuss the behavior of energy density and pressure distribution for both models. Moreover, we analyze different physical properties such as behavior of energy density and pressure, equilibrium conditions, equation of state parameters, causality conditions and adiabatic index. It is noticed that both $f(R)$ gravity models are suitable and provides viable results with Bardeen geometry.