Relativistic Tidal Disruption in Black Hole and Wormhole Backgrounds

Abstract

Black holes (BHs) and wormholes (WHs) are characterized by distinct spacetime geometries, whose differences become pronounced close to the central objects. A useful way to probe such differences is via the dynamics of stellar tidal disruption events in the regime of strong gravity. Here, using a general relativistic smoothed particle hydrodynamics code inspired from an algorithm developed by Liptai and Price, we perform a suite of numerical simulations of solar mass polytropic stars in the background of supermassive Schwarzschild BHs and similar mass exponential WHs. Important differences between the two geometries near the BH event horizon or the WH throat is provided by the distinct outcomes of such events. For a given impact parameter, BH backgrounds lead to greater tidal stripping compared to WHs ones and further, the critical impact parameter, beyond which the star undergoes full tidal disruption is higher for WH backgrounds compared to BHs. We further study the differences in observable peak fallback rates in the two backgrounds. We also provide a quantitative explanation for the tendency of stars in partial tidal disruptions to retain larger cores around more massive centers, by computing tidal stresses in a Fermi normal coordinate system and introducing an appropriate measure of stellar compactness. Finally, we suggest a way to observationally distinguish BH and WH backgrounds, based on the properties of different observables.

Figures (17)

• Figure 1: Evolution of debris around BH (left column) and WH (right column) of $1.2 \times 10^7 M_\odot$, $\beta = 1.3$ ($r_p \approx 6.9 r_g$). Log density (in $g\,cm^{-2}$) is shown via the color bar. A remnant self-bound core is visible at $t = 0.55$ days in the WH case (bottom right), indicating partial disruption.
• Figure 2: Bound core mass fraction, $M_{\rm bound}/M_\ast$, as a function of periapsis-normalized time, $t/t_p$, for BH (solid lines) and WH (dashed lines) encounters. Panels (A) and (B) correspond to $M_\bullet = 6\times 10^6\,M_{\odot}$, while panels (C) and (D) correspond to $M_\bullet = 1.1\times 10^7\,M_{\odot}$. Each panel shows two values of the impact parameter $\beta$, as indicated in the legends. In all cases the WH consistently retaining a larger bound core compared to the BH for the same $\beta$.
• Figure 3: Critical periapsis distance and critical impact parameter as functions of the BH and WH mass, $M_\bullet$, shown in units of $10^6\,M_\odot$. Panel (A) shows the critical periapsis distance, $r_{p,c}/r_g$, and panel (B) shows the critical impact parameter, $\beta_c$, for the BH and WH cases. The red points and solid curves correspond to the BH data and fit, while the black points and dashed curves correspond to the WH data and fit, respectively.
• Figure 4: Fallback rate, $\dot{M}$, as a function of time, $t$, for BH (solid red) and WH (dashed black) cases. Panel (A) corresponds to $M_\bullet = 6\times 10^6\,M_\odot$, $\beta = 1.0$, and panel (B) to $M_\bullet = 1.1\times 10^7\,M_\odot$, $\beta = 1.1$, with reference slopes $t^{-5/3}$ and $t^{-9/4}$ shown. The WH case exhibits a steeper late-time decay compared to the BH.
• Figure 5: Energy distribution, $dM/d\epsilon$, as a function of normalized energy, $\epsilon/\Delta\epsilon$, for the BH (solid red) and WH (dashed black) cases. Panel (A) corresponds to $M_\bullet = 6\times 10^6\,M_\odot$, $\beta = 1.0$, and panel (B) to $M_\bullet = 1.1\times 10^7\,M_\odot$, $\beta = 1.1$. The WH case shows a suppressed and split distribution near $\epsilon \sim 0$, while the BH case remains more centrally peaked.