Formation of Bound States in Quintessence Alternative Theories

TL;DR

This work analyzes bound states of scalar perturbations outside the horizon of a quintessence-dressed AdS black hole by deriving a generalized Regge-Wheeler equation and associated potentials. It shows that quintessence, via parameters $a$ and $w$, modifies the background metric and Hawking temperature, which in turn shape the Regge-Wheeler potential and the existence of bound states. Bound-state masses emerge only for sufficiently large $|w|$ and/or angular momentum $l$, with masses increasing approximately linearly with $a$ and bandwidths decreasing for higher $l$, while charge $Q$ can suppress bound-state formation. The results bridge black-hole thermodynamics, quintessence physics, and quantum bound-state phenomena, suggesting cosmological implications and guiding future studies of quasinormal modes in such backgrounds.

Abstract

We study the formation and behaviour of bound states formed outside the horizon of a black hole in the presence of quintessence matter. Calculating the Regge and Wheeler potential for general metric function, we find that the presence of quintessence influences significantly the metric function and the Hawking temperature. We show that large black holes radiate less in the presence of quintessence matter and it seems to live longer, while small black holes radiate more in comparison with the model in the absence of quintessence. Bound states emerge at large enough quintessence parameter $|w|$ or angular momentum.

Figures (7)

• Figure 1: (a) Metric function $g\equiv f(r)$ versus $r$ for $Q=0.00,$$w=-0.80$ and $a=0.20,$ (blue curve, highest) $a=0.40$ (purple curve) $a=0.60$ (brown curve) and $a=0.80$ (cyan curve, lowest). (b) Metric function $g\equiv f(r)$ versus $r$ for $Q=0.00,$$a=0.80$ and $w=-0.40,$ (blue curve, highest on the right part) $w=-0.60$ (purple curve) $w=-0.80$ (brown curve) and $w=-1.00$ (cyan curve, lowest on the right part). (c) Metric function $g\equiv f(r)$ versus $r$ for $Q=0.20,$$w=-0.80$ and $a=0.20,$ (blue curve, highest) $a=0.40$ (purple curve) $a=0.60$ (brown curve) and $a=0.80$ (cyan curve,lowest). (d) Metric function $g\equiv f(r)$ versus $r$ for $Q=0.20,$$a=0.80$ and $w=-0.40,$ (blue curve, highest on the right part) $w=-0.60$ (purple curve) $w=-0.80$ (brown curve) and $w=-1.00$ (cyan curve, lowest on the right part).
• Figure 2: (a) Temperature versus $r_h\equiv r_+$ for $Q=0.00,$$w=-0.80$ and $a=0.20,$ (blue curve, highest) $a=0.40$ (purple curve) $a=0.60$ (brown curve) and $a=0.80$ (cyan curve, lowest). (b) Temperature versus $r_h\equiv r_+$ for $Q=0.00,$$a=0.80$ and $w=-0.40,$ (blue curve, highest on the right part) $w=-0.60$ (purple curve) $w=-0.80$ (brown curve) and $w=-1.00$ (cyan curve, lowest on the right part). (c) Temperature versus $r_h\equiv r_+$ for $Q=0.20,$$w=-0.80$ and $a=0.20,$ (blue curve, highest) $a=0.40$ (purple curve) $a=0.60$ (brown curve) and $a=0.80$ (cyan curve, lowest). (d) Temperature versus $r_h\equiv r_+$ for $Q=0.20,$$a=0.80$ and $w=-0.40,$ (blue curve, highest on the right part) $w=-0.60$ (purple curve) $w=-0.80$ (brown curve) and $w=-1.00$ (cyan curve, lowest on the right part).
• Figure 3: Left panel: Potentials for $a=0,\ l=0,\ M=0.05$ and four values of the charge: $Q=0.00$ (pink curve, highest), $Q=0.04$ (blue curve), $Q=0.07$ (khaki curve) and $Q=0.10$ (green curve, lowest). Right panel: Potentials for $a=0.8,\ w=-0.80,\ M=0.05$ and $Q=0.00$ (pink curve, highest), $Q=0.04$ (blue curve), $Q=0.07$ (khaki curve) and $Q=0.10$ (green curve, lowest).
• Figure 4: Left panel: Potentials for $a=0.8,\ l=0,\ M=0.05,\ Q=0.00,$ and four values for the parameter $w:$$w=-0.40$ (blue curve, no left barrier), $w=-0.60$ (pink curve), $w=-0.80$ (khaki curve) and $w=-1.00$ (green curve, highest left barrier). Right panel: Same as in the left panel, but $Q=0.04.$
• Figure 5: Left panel: Potentials for $a=0.8,\ M=0.05,\ Q=0.00,\ w=-0.60$ and three values for the angular momentum: $l=0$ (blue curve, lowest), $l=1$ (pink curve), and $l=2$ (green curve, highest). Right panel: Potentials for $l=0,\ M=0.05,\ Q=0.00,\ w=-0.60$ and four values for the parameter $a:$$a=0.2$ (blue curve, highest), $a=0.4$ (pink curve), $a=0.6$ (khaki curve), and $a=0.8$ (green curve, lowest).