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We consider dynamics of a quantum scalar field, minimally coupled to classical gravity, in the near-horizon region of a Schwarzschild black-hole. It is described by a static Klein-Gordon operator which in the near-horizon region reduces to a scale invariant Hamiltonian of the system. This Hamiltonian is not essentially self-adjoint, but it admits a one-parameter family of self-adjoint extension. The time-energy uncertainty relation, which can be related to the thermal black-hole mass fluctuations, requires explicit construction of a time operator near-horizon. We present its derivation in terms of generators of the affine group. Matrix elements involving the time operator should be evaluated in the affine coherent state representation.
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We study dynamics of a scalar field in the near-horizon region described by a static Klein-Gordon operator which is the Hamiltonian of the system. The explicite construction of a time operator near-horizon is given and its self-adjointness discussed.
In this article, we study Beltrami equilibria for plasmas in near the horizon of a spinning black hole, and develop a framework for constructing the magnetic field profile in the near horizon limit for Clebsch flows in the single-fluid approximation. We find that the horizon profile for the magnetic field is shown to satisfy a system of first-order coupled ODEs dependent on a boundary condition for the magnetic field. For states in which the generalized vorticity vanishes (the generalized `superconducting plasma state), the horizon profile becomes independent of the boundary condition, and depend only on the thermal properties of the plasma. Our analysis makes use of the full form for the time-independent Amperes law in the 3+1 formalism, generalizing earlier conclusions for the case of vanishing vorticity, namely the complete magnetic field expulsion near the equator of an axisymmetric black horizon assuming that the thermal properties of the plasma are symmetric about the equatorial plane. For the general case, we find and discuss additional conditions required for the expulsion of magnetic fields at given points on the black hole horizon. We perform a length scale analysis which indicates the emergence of two distinct length scales characterizing the magnetic field variation and strength of the Beltrami term, respectively.
We examine the non-inertial effects of a rotating frame on a Dirac oscillator in a cosmic string space-time with non-commutative geometry in phase space. We observe that the approximate bound-state solutions are related to the biconfluent Heun polynomials. The related energies cannot be obtained in a closed form for all the bound states. We find the energy of the fundamental state analytically by taking into account the hard-wall confining condition. We describe how the ground-state energy scales with the new non-commutative term as well as with the other physical parameters of the system.
We analyze and compute the semiclassical stress-energy flux components, the outflux $langle T_{uu}rangle$ and the influx $langle T_{vv}rangle$ ($u$ and $v$ being the standard null Eddington coordinates), at the inner horizon (IH) of a Reissner-Nordstrom black hole (BH) of mass $M$ and charge $Q$, in the near-extremal domain in which $Q/M$ approaches $1$. We consider a minimally-coupled massless quantum scalar field, in both Hartle-Hawking ($H$) and Unruh ($U$) states, the latter corresponding to an evaporating BH. The near-extremal domain lends itself to an analytical treatment which sheds light on the behavior of various quantities on approaching extremality. We explore the behavior of the three near-IH flux quantities $langle T_{uu}^-rangle^U$, $langle T_{vv}^-rangle^U$, and $langle T_{uu}^-rangle^H=langle T_{vv}^-rangle^H$, as a function of the small parameter $Deltaequivsqrt{1-(Q/M)^2}$ (where the superscript $-$ refers to the IH value). We find that in the near-extremal domain $langle T_{uu}^-rangle^Uconglangle T_{uu}^-rangle^H=langle T_{vv}^-rangle^H$ behaves as $proptoDelta^5$. In contrast, $langle T_{vv}^-rangle^U$ behaves as $proptoDelta^4$, and we calculate the prefactor analytically. It therefore follows that the semiclassical fluxes at the IH neighborhood of an evaporating near-extremal spherical charged BH are dominated by the influx $langle T_{vv}rangle^U$. In passing, we also find an analytical expression for the transmission coefficient outside a Reissner-Nordstrom BH to leading order in small frequencies (which turns out to be a crucial ingredient of our near-extremal analysis). Furthermore, we explicitly obtain the near-extremal Hawking-evaporation rate ($proptoDelta^4$), with an analytical expression for the prefactor (obtained here for the first time to the best of our knowledge). [Abridged]
There is growing notion that black holes may not contain curvature singularities (and that indeed nature in general may abhor such spacetime defects). This notion could have implications on our understanding of the evolution of primordial black holes (PBHs) and possibly on their contribution to cosmic energy. This paper discusses the evolution of a non-singular black hole (NSBH) based on a recent model [1]. We begin with a study of the thermodynamic process of the black hole in this model, and demonstrate the existence of a maximum horizon temperature T_{max}, corresponding to a unique mass value. At this mass value the specific heat capacity C changes signs to positive and the body begins to lose its black hole characteristics. With no loss of generality, the model is used to discuss the time evolution of a primordial black hole (PBH), through the early radiation era of the universe to present, under the assumption that PBHs are non-singular. In particular, we track the evolution of two benchmark PBHs, namely the one radiating up to the end of the cosmic radiation domination era, and the one stopping to radiate currently, and in each case determine some useful features including the initial mass m_{f} and the corresponding time of formation t_{f}. It is found that along the evolutionary history of the universe the distribution of PBH remnant masses (PBH-RM) PBH-RMs follows a power law. We believe such a result can be a useful step in a study to establish current abundance of PBH-MRs.
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