General Relativity and Quantum Cosmology (gr-qc)

Abstract: We consider the non-commutative(NC) Kerr black hole where the mass of the central object is smeared over a region of linear size $\sqrt{b}$, $b$ is the strength of the NC character of spacetime. For the spacetime under consideration, we calculate the amplification factor for scalar, electromagnetic, and gravitational fields, and study various properties of a thin accretion disk. The expression for the amplification factor is obtained with the help of the asymptotic matching technique. The amplification factor is then plotted against frequency for various values of the spin $a$ and the NC parameter $b$. We find that though the amplification factor increases with $a$ but decreases with $b$, the cut-off frequency up to which we have amplification increases with $a$ and $b$. We then study the effect of the spin and the NC nature of spacetime on the energy flux, temperature distribution, emission spectrum, energy conversion efficiency, and the radius of the innermost stable circular orbit of a thin accretion disk around the black hole with the help of the steady-state Novikov-Thorne model. Our study reveals that these quantities increase with the spin and the NC parameter. We also find that the disk around the NC Kerr black is hotter and more luminous than that around the Kerr black hole and the NC Schwarzschild black hole. We can conclusively infer from our investigation that the NC nature of spacetime has a significant impact on the superradiance phenomenon as well as on various properties of thin accretion disks.

Abstract: The 2023 second edition of a 2006 encyclopedia article on mathematical aspects of quantum field theory in curved spacetimes (QFTCST). Section titles [with titles of newly added subsections in square brackets] are: Introduction and preliminaries; Construction of a *-algebra for a real linear scalar field on globally hyperbolic spacetimes and some general theorems, [More about (quasifree) Hadamard states]; Particle creation and the limitations of the particle concept; Theory of the stress-energy tensor; More about the intersection of QFTCST with AQFT and the Fewster-Verch No-Go Theorem; Hawking and Unruh effects, [More about (classical and) quantum fields on black hole backgrounds]; Non-globally hyperbolic spacetimes and the time-machine question, [More about QFT on non-globally hyperbolic spacetimes]; Other related topics and some warnings. The article contains many references. It also includes a review of, and also compares and contrasts, recent results on the implications of QFTCST for the question of the instability of three sorts of Cauchy horizon -- first those inside black holes such as especially Reissner-Nordstr\"om-de Sitter and Kerr-de Sitter, second the compactly generated Cauchy horizons of spacetimes in which time-machines get manufactured, and third the Cauchy horizon of the spacetime diagram which is believed to describe evaporating black holes and which underlies (one version of) the black hole information-loss puzzle.