  With the precision now afforded by modern space-based photometric
observations from the retired K2 and current TESS missions, the effects of
general relativity (GR) may be detectable in the light curves of pulsating
white dwarfs (WDs). Almost all WD models are calculated using a Newtonian
description of gravity and hydrodynamics. To determine if inclusion of GR leads
to observable effects, we used idealized models of compact stars and made
side-by-side comparison of mode periods computed using a (i) Newtonian and (ii)
GR description of the equilibrium structure and nonradial pulsations. For
application to white dwarfs, it is only necessary to include the first
post-Newtonian (1PN) approximation to GR. The mathematical nature of the linear
nonradial pulsation problem is then qualitatively unchanged and the GR
corrections can be written as extensions of the classic Dziembowski equations.
As such, GR effects might easily be included in existing asteroseismology
codes. The idealized stellar models are (i) \pn1 relativistic polytropes and
(ii) stars with cold degenerate-electron equation of state featuring a
near-surface chemical transition from $\mu_e = 2$ to $\mu_e = 1$, simulating a
surface hydrogen layer. Comparison of Newtonian and 1PN normal mode periods
reveals fractional differences on the order of the surface gravitational
redshift $z$. For a typical WD, this fractional difference is $\sim 10^{-4}$
and is greater than the period uncertainty $\sigma_{\Pi}/\Pi$ of many white
dwarf pulsation modes observed by TESS. A consistent theoretical modeling of
periods observed in these stars should in principle include GR effects to 1PN
order.
