  The spin state of small asteroids can change on a long timescale by the
Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, the net torque that arises
from anisotropically scattered sunlight and proper thermal radiation from an
irregularly-shaped asteroid. The secular change in the rotation period caused
by the YORP effect can be detected by analysis of asteroid photometric
lightcurves. We analyzed photometric lightcurves of near-Earth asteroids (1865)
Cerberus, (2100) Ra-Shalom, and (3103) Eger with the aim to detect possible
deviations from the constant rotation caused by the YORP effect. We carried out
new photometric observations of the three asteroids, combined the new
lightcurves with archived data, and used the lightcurve inversion method to
model the asteroid shape, pole direction, and rotation rate. The YORP effect
was modeled as a linear change in the rotation rate in time d\omega /dt. Values
of d\omega/ dt derived from observations were compared with the values
predicted by theory. We derived physical models for all three asteroids. We had
to model Eger as a nonconvex body because the convex model failed to fit the
lightcurves observed at high phase angles. We probably detected the
acceleration of the rotation rate of Eger d\omega / dt = (1.4 +/- 0.6) x
10^{-8} rad/d (3\sigma error), which corresponds to a decrease in the rotation
period by 4.2 ms/yr. The photometry of Cerberus and Ra-Shalom was consistent
with a constant-period model, and no secular change in the spin rate was
detected. We could only constrain maximum values of |d\omega / dt| < 8 x
10^{-9} rad/d for Cerberus, and |d\omega / dt| < 3 x 10^{-8} rad/d for
Ra-Shalom.
