On the effect of scalar fields on Hawking radiation and quasinormal modes of black holes

Chowdhury, Avijit (2021) On the effect of scalar fields on Hawking radiation and quasinormal modes of black holes. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Avijit Chowdhury (13IP001)) 13IP001.pdf - Submitted Version Restricted to Repository staff only Download (3MB)

Abstract

The present thesis attempts to study the effect of scalar fields on Hawking radiation and quasinormal modes of black holes. We selected a static, spherically symmetric electrically charged black hole with an additional scalar ‘hair’ for our analysis. The scalar ‘hair’ is sourced by a scalar field, conformally coupled to the Einstein-Hilbert action. The scalar field can survive even in the absence of the black hole’s electric charge and is characterized as a ‘primary hair’. This scalar field changes the gravitational constant, and hence modifies the ADM (Arnowitt-Deser-Missner) mass of the black hole. The scalar field’s strength is determined by a scalar ‘charge’ that manifests itself as an additive correction to the square of the electric charge in the standard Reissner-Nordstr¨om metric. This seemingly simple modification leads to nontrivial physical implications. We start with an analysis of the quasinormal modes of the black hole mentioned above against perturbation by massless and massive, uncharged and charged scalar and Dirac test fields. The quasinormal modes encode a black hole’s response to perturbations (either of the metric or that induced by a test field). The quasinormal modes are characterized by damped oscillations with complex frequencies called the Quasinormal frequencies. The real part of the quasinormal frequency gives the actual frequency of the wave motion, whereas the imaginary part corresponds to the damping rate. We observed that the presence of the scalar hair affects both the real part and imaginary part of the quasinormal frequency. If one relaxes the quasinormal mode boundary conditions of purely ingoing waves at the event horizon and purely outgoing waves at spatial infinity and instead considers a charged bosonic wave incident on the black hole from spatial infinity, then the reflected wave from the event horizon may be amplified. This superradiant amplification occurs at the cost of the electrical (or rotational in case of rotating black hole) energy of the black hole. The superradiantly amplified waves can be confined and made to interact repeatedly with the black hole by a hypothetical ‘mirror’ surrounding the black hole. This repeated reflection and superradiance may lead to an exponentially increasing amplitude and hence instability. Interestingly, the mass of the incident bosonic wavefield can effectively act as a ‘mirror’ to reflect the low-frequency modes and lead to superradiant instability. We studied the effect of the scalar hair on the superradiant stability of the black hole. An isolated black hole is also capable of radiating via pair-production in the form of Hawking radiation. To an asymptotic observer, the Hawking emission spectrum ‘coarsely resembles’ a black body spectrum with a temperature inversely proportional to the black hole’s mass. Though detection of Hawking radiation from astrophysical black holes is a near impossibility due to the extremely low temperature of the black holes, the study of Hawking radiation is significant in its own right, particularly in the pursuit to arrive at a quantum theory of gravity. The Hawking radiation emitted at the event horizon gets modified as it propagates through the spacetime surrounding the black hole, which acts as a filter, allowing only a fraction of the emitted radiation to reach an asymptotic observer. This fraction is referred to as the Greybody factor and measures the deviation of the Hawking emission spectrum from perfect blackbody like Planckian distribution. Another critical aspect that distinguishes Hawking radiation from blackbody radiation is its ‘sparsity’, which measures the number of particles emitted per unit time. Whereas the sparsity of a blackbody spectrum is extremely low, suggesting an enormous number of emitted particles per unit time, the sparsity of the Hawking radiation is exceptionally high. The latter half of the thesis is devoted to studying the effect of the black hole scalar hair on Hawking radiation of scalar particles, its sparsity, and greybody factor.

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