General Relativity And Quantum Cosmology

By considering a small correction to the Maxwell field, we show that the resultant black hole solutions (also known as the asymptotically Reissner--Nordström black holes) undergo the reentrant phase transition and can have a novel phase behavior. We also show that such a small nonlinear correction of the Reissner--Nordström black holes has high effects on the phase structure of the solutions. It leads to a new classification in the canonical ensemble of extended phase space providing the values of the nonlinearity parameter α being α�? q 2 /7 . We shall study these three classes and investigate deviations from those of the standard Reissner--Nordström solutions. Interestingly, we find that there is the reentrant phase transition for α<4 q 2 /7 , and for the case of α=4 q 2 /7 there is no phase transition below (at) the critical point. For the last case, one finds that small and large black holes are thermodynamically distinguishable for temperatures and pressures higher than the critical ones.

It is well known that the inflationary scenario often displays different sets of degeneracies in its predictions for CMB observables. These degeneracies usually arise either because multiple inflationary models predict similar values for the scalar spectral index n S and the tensor-to-scalar ratio r , or because within the same model, the values of { n S ,r} are insensitive to some of the model parameters, making it difficult for CMB observations alone to constitute a unique probe of inflationary cosmology. We demonstrate that by taking into account constraints on the post-inflationary reheating parameters such as the duration of reheating N re , its temperature T re and especially its equation of state (EOS), w re , it is possible to break this degeneracy in certain classes of inflationary models where identical values of { n S ,r} can correspond to different reheating w re . In particular, we show how reheating constraints can break inflationary degeneracies in the T-model and the E-model α -attractors. Non-canonical inflation is also studied. The relic gravitational wave (GW) spectrum provides us with another tool to break inflationary degeneracies. This is because the GW spectrum is sensitive to the post-inflationary EOS of the universe. Indeed a stiff EOS during reheating ( w re >1/3) gives rise to a small scale blue tilt in the spectral index n GW = dlog Ω GW dlogk >0 , while a soft EOS ( w re <1/3) results in a red tilt. Relic GWs therefore provide us with valuable information about the post-inflationary epoch, and their spectrum can be used to cure inflationary degeneracies in { n S ,r} .

We study curvature invariants in a binary black hole merger. It has been conjectured that one could define a quasi-local and foliation independent black hole horizon by finding the level-- 0 set of a suitable curvature invariant of the Riemann tensor. The conjecture is the geometric horizon conjecture and the associated horizon is the geometric horizon. We study this conjecture by tracing the level-- 0 set of the complex scalar polynomial invariant, D , through a quasi-circular binary black hole merger. We approximate these level-- 0 sets of D with level-- ε sets of |D| for small ε . We locate the local minima of |D| and find that the positions of these local minima correspond closely to the level-- ε sets of |D| and we also compare with the level-- 0 sets of Re(D) . The analysis provides evidence that the level-- ε sets track a unique geometric horizon. By studying the behaviour of the zero sets of Re(D) and Im(D) and also by studying the MOTSs and apparent horizons of the initial black holes, we observe that the level-- ε set that best approximates the geometric horizon is given by ε= 10 ?? .

Cuspy shadow was first reported for hairy rotating black holes, whose metrics deviate significantly from the Kerr one. The non-smooth edge of the shadow is attributed to a transition between different branches of unstable but bounded orbits, known as the fundamental photon orbits, which end up at the light rings. In searching for a minimal theoretical setup to reproduce such a salient feature, in this work, we devise a toy model with axisymmetry, a slowly rotating Kerr black hole enveloped by a thin slowly rotating dark matter shell. Despite its simplicity, we show rich structures regarding fundamental photon orbits explicitly in such a system. We observe two disconnected branches of unstable spherical photon orbits, and the jump between them gives rise to a pair of cusps in the resultant black hole shadow. Besides the cuspy shadow, we explore other intriguing phenomena when the Maxwell construction cannot be established. We find that it is possible to have an incomplete arc of Einstein rings and a "fractured" shadow. The potential astrophysical significance of the corresponding findings is addressed.

The Geroch/Stephani transformation is a solution-generating transformation, and may generate spiky solutions. The spikes in solutions generated so far are either early-time permanent spikes or transient spikes. We want to generate a solution with a late-time permanent spike. We achieve this by applying Stephani's transformation with the rotational Killing vector field of the locally rotationally symmetric Jacobs solution. The late-time permanent spike occurs along the cylindrical axis. Using a mixed Killing vector field, the generated solution also features a rich variety of transient structures. We introduce a new technique to analyse these structures. Our findings lead us to discover a transient behaviour, which we call the overshoot transition. These discoveries compel us to revise the description of transient spikes.

We investigate various dark energy models by taking into account the thermal effects induced from Hawking radiation on the apparent horizon of the Universe, for example near a finite-time future singularity. If the dark energy density increases as the Universe expands, the Universe's evolution reaches a singularity of II type (or sudden future singularity). The second derivative of scale factor diverges but the first remains finite. Quasi-de Sitter evolution can change on sudden future singularity in the case of having an effective cosmological constant larger than the maximum possible value of the energy density of the Universe. Another interesting feature of cosmological solution is the possibility of a transition between deceleration and acceleration for quintessence dark energy with a simple equation of state. Finally, we investigate which fluid component can remedy Big Rip singularities and other crushing type singularities.

The aim of this paper is to provide the geometrical structure of a gravitational field that includes the addition of dark matter in the framework of a Riemannian and a Riemann--Sasaki spacetime. By means of the classical Riemannian geometric methods we arrive at modified geodesic equations, tidal forces, and Einstein and Raychaudhuri equations to account for extra dark gravity. We further examine an application of this approach in cosmology. Moreover, a possible extension of this model on the tangent bundle is studied in order to examine the behavior of dark matter in a unified geometric model of gravity with more degrees of freedom. Particular emphasis shall be laid on the problem of the geodesic motion under the influence of dark matter.

Neutron stars could contain a mixture of ordinary nuclear matter and dark matter, such that dark matter could influence observable properties of the star, such as its mass and radius. We study these dark matter admixed neutron stars for two choices of dark matter: a free Fermi gas and mirror dark matter. In addition to solving the multi-fluid Tolmon-Oppenheimer-Volkoff equations for static solutions and presenting mass-radius diagrams, we focus on two computations that are lacking in the literature. The first is a rigorous determination of stability over the whole of parameter space, which we do using two different methods. The first method is based on harmonic time-dependent perturbations to the static solutions and on solving for the radial oscillation frequency. The second method, which is less well-known, conveniently makes use of unperturbed, static solutions only. The second computation is of the radial oscillation frequency, for fundamental modes, over large swaths of parameter space.

The vorticity of world lines of observers associated to the rotation of a massive body was reported by Lense and Thirring more than a century ago. In their example the frame dragging effect induced by the vorticity, is directly (explicitly) related to the rotation of the source. However in many other cases it is not so, and the origin of vorticity remains obscure and difficult to identify. Accordingly, in order to unravel this issue, and looking for the ultimate origin of vorticity associated to frame dragging, we analyze in this manuscript very different scenarios where frame dragging effect is present. Specifically we consider general vacuum stationary spacetimes, general electro-vacuum spacetimes, radiating electro-vacuum spacetimes and Bondi--Sachs radiating spacetimes. We identify the physical quantities present in all these cases, which determine the vorticity and may legitimately be considered as responsible for the frame dragging. Doing so we provide a comprehensive physical picture of frame dragging. Some observational consequences of our results are discussed.

The symmetries of asymptotically flat spacetimes in general relativity are given by the Bondi-Metzner-Sachs (BMS) group, though there are proposed generalizations of its symmetry algebra. Associated with each symmetry is a charge and a flux, and the values of these charges and their changes can characterize a spacetime. The charges of the BMS group are relativistic angular momentum and supermomentum (which includes 4-momentum); the extensions of the BMS algebra also include generalizations of angular momentum called "super angular momentum." Several different formalisms have been used to define angular momentum, and they produce nonequivalent expressions for the charge. It was shown recently that these definitions can be summarized in a two-parameter family of angular momenta, which we investigate in this paper. We find that requiring that the angular momentum vanishes in flat spacetime restricts the two parameters to be equal. If we do not require that the angular momentum agrees with a Hamiltonian definition, then there is no clear reason to fix the remaining free parameter to a particular value. We then also propose a similar two-parameter family of super angular momentum. We examine the effect of the free parameters on the values of the angular momentum and super angular momentum from nonprecessing binary-black-hole mergers. The definitions of angular momentum differ at a high post-Newtonian order for these systems, but only when the system is radiating gravitational waves (not before and after). The different super-angular-momentum definitions occur at lower orders, and there is a difference in the change of super angular momentum even after the gravitational waves pass, which arises because of the gravitational-wave memory effect. We estimate the size of these effects using numerical-relativity surrogate waveforms and find they are small but resolvable.