Scalar tachyonic instabilities in gravitational backgrounds: Existence and growth rate

L. Perivolaropoulos; F. Skara

doi:10.1103/PhysRevD.102.104034

paper

Scalar tachyonic instabilities in gravitational backgrounds: Existence and growth rate

arXiv:2009.05640 · doi:10.1103/PhysRevD.102.104034

Abstract

It is well known that the Klein Gordon (KG) equation $□ Φ + m^{2} Φ = 0$ has tachyonic unstable modes on large scales ( $k^{2} < ∣ m ∣^{2}$ ) for $m^{2} < m_{cr}^{2} = 0$ in a flat Minkowski spacetime with maximum growth rate $Ω_{F} (m) = ∣ m ∣$ achieved at $k = 0$ . We investigate these instabilities in a Reissner-Nordström-deSitter (RN-dS) background spacetime with mass $M$ , charge $Q$ , cosmological constant $Λ > 0$ and multiple horizons. By solving the KG equation in the range between the event and cosmological horizons, using tortoise coordinates $r_{*}$ , we identify the bound states of the emerging Schrodinger-like Regge-Wheeler equation corresponding to instabilities. We find that the critical value $m_{cr}$ such that for $m^{2} < m_{cr}^{2}$ bound states and instabilities appear, remains equal to the flat space value $m_{cr} = 0$ for all values of background metric parameters despite the locally negative nature of the Regge-Wheeler potential for $m = 0$ . However, the growth rate $Ω$ of tachyonic instabilities for $m^{2} < 0$ gets significantly reduced compared to the flat case for all parameter values of the background metric ( $Ω (Q / M, M^{2} Λ, m M) < ∣ m ∣$ ). This increased lifetime of tachyonic instabilities is maximal in the case of a near extreme Schwarzschild-deSitter (SdS) black hole where $Q = 0$ and the cosmological horizon is nearly equal to the event horizon ( $ξ \equiv 9 M^{2} Λ ≃ 1$ ). The physical reason for this delay of instability growth appears to be the existence of a cosmological horizon that tends to narrow the negative range of the Regge-Wheeler potential in tortoise coordinates.

arXiv comment19 pages, 10 figures. References added, typos corrected. The Mathematica numerical file that lead to the production of the figures may be downloaded from http://leandros.physics.uoi.gr/tachyonic-instabilities.zip

Scalar tachyonic instabilities in gravitational backgrounds: Existence and growth rate

Abstract

References in corpus (114)

Cited by in corpus (3)